*4.1. Distribution Transformer Basic Parameters*

According to Table 2, there are 13 key state quantities of distribution transformers, including four quantitative indicators and nine qualitative indicators. To reduce data redundancy and clearly show the accuracy of the algorithm, Table 6 shows the rating of the five major factor sets of the distribution transformer, including a quantitative indicator: winding DC resistance; and four qualitative indicators: sealing performance μ1, insulation performance μ2, grounding situation μ6 and marking situation μ8.

### *4.2. Status Assessment of Distribution Transformers*

According to the basic principle of the compromised fuzzy decision, the qualitative indicators (excellent, good, qualified, unqualified) are firstly analyzed according to the quantitative indicators. The quantitative criteria are shown in Table 7.


**Table 6.** The original data of distribution transformer.

**Table 7.** Quantitative standard for qualitative index of distribution transformers.


The initial triangle weight value is:

$$\mathcal{W} = \begin{bmatrix} (0.5, 0.5, 0.5) \\ (0.2, 0.2, 0.2) \\ (0.15, 0.15, 0.15) \\ (0.1, 0.1, 0.1) \\ (0.05, 0.05, 0.05) \end{bmatrix}^T$$

The index information and the weight information are transformed into triangular fuzzy numbers, and the fuzzy index matrix *F* is obtained as follows.


The data in *F* is normalized to obtain the fuzzy decision matrix *D*. According to Equation (10), the fuzzy positive ideal *M*<sup>+</sup> and the fuzzy negative ideal *M*− are obtained as:

$$\boldsymbol{M}^{+} = \begin{bmatrix} (0.5, 0.5, 0.5) \\ (0.17, 0.20, 0.20) \\ (0.1275, 0.15, 0.15) \\ (0.085, 0.1, 0.1) \\ (0.0425, 0.05, 0.05) \end{bmatrix}^{T} \boldsymbol{M}^{-} = \begin{bmatrix} (0.4531, 0.4531, 0.4531) \\ (0.1, 0.1222, 0.1412) \\ (0.0750, 0.0917, 0.1059) \\ (0.05, 0.0611, 0.0706) \\ (0.03, 0.0389, 0.0441) \end{bmatrix}^{T} \boldsymbol{M}^{-}$$

The fuzzy double peak value and the membership percentage value obtained by the fuzzy optimization decision after multiple times of the cycle are shown in Table 8, and finally, the state evaluation value of the distribution transformer is obtained.


**Table 8.** Results of distribution transformer status assessment.

The fuzzy positive ideal and the fuzzy negative ideal are determined by analyzing a large number of transformers of the same type. This paper adopts a combination of eclectic fuzzy decision-making and multilevel fuzzy comprehensive evaluation, and the weights of quantitative indicators and qualitative indicators can be obtained by performing repeated fuzzy iterations. The weight ratio of the evaluation set is constantly updated through the weight inverse operation, reducing the influence of subjective factors brought by the expert review opinions and avoiding errors caused by data redundancy or errors or omissions, which improving the reliability of data analysis and promoting the establishment of the weight expert database, finally. The distances between the evaluated object and the fuzzy positive and negative ideals are determined, and the membership degree belonging to the fuzzy positive ideal is calculated. The greater the membership degree, the better the state of the transformer. The smaller the membership degree, the worse the state of the transformer, so it is necessary for the operation and maintenance personnel to pay attention to it and arrange the maintenance work in good time. The comparison and analysis of the relevant data in Tables 6 and 8 show that the final score of each transformer in Table 8 can truly reflect the actual operation status of the transformer in Table 6, which provides quantitative parameters for the evaluation of distribution equipment, and which is beneficial to the further focus and field evaluation of the equipment, providing help for maintenance and operation.

The analysis of practical examples shows that the evaluation method is concise and intuitionistic, and the evaluation conclusion not only reflects the state of a single transformer, but also facilitates the ranking of the overall state of the transformer, which provides reasonable suggestions for orderly arrangemen<sup>t</sup> of transformer maintenance.
